In Table REF  we summarize the proven minimal integration orders for system and adjoint equations derived in this paper and in [1]}. It follows that if a state trajectory includes sections with sliding modes then the reduced gradient can be approximated with the accuracy at least \(O(h^2)\) , otherwise the accuracy is at least \(O(h^3)\) . This accuracy estimate takes into account the fact that if a discrete state changes then we have to start the integration of system and adjoint equations with the perturbed initial values of system and adjoint variables respectively—the influence of that perturbation on the accuracy of system and adjoint variables determination follows from Theorem 4.3 in [2]} (cf. (120)–(121) and (139) in [1]}), or from Theorem 4.2 in [4]} (cf. (REF )–() and (REF )–()).
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